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Full-Order Reconstruction of Simplicial Complex Network from Binary Time Series.

Ziqi Yang1, Yi Zhao1, Michael Small2,3

  • 1Harbin Institute of Technology, School of Science, Shenzhen 518055, China.

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|May 11, 2026
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Summary

We developed a data-driven method to infer complex network structures from observational data. This approach accurately reconstructs high-order network topologies using only node states.

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Area of Science:

  • Complex systems science
  • Network science
  • Data science

Background:

  • Inferring complex network structures from observational data is challenging.
  • Existing methods struggle with high-order topologies and solely using node states.

Purpose of the Study:

  • To propose a versatile and precise framework for inferring full-order network structures from node states.
  • To reconstruct underlying topological structures using a data-driven approach.

Main Methods:

  • A data-driven likelihood optimization framework is proposed.
  • The method captures state transition relationships in binary time series from Markovian dynamics.
  • The difference of convex algorithm is employed for efficient full-order reconstruction.

Main Results:

  • The approach successfully reconstructs a full-order simplicial network.
  • High accuracy was achieved across various experimental conditions.
  • The method demonstrates effectiveness in uncovering complex interactions.

Conclusions:

  • The proposed framework offers a precise and versatile solution for inferring complex network structures.
  • This data-driven approach has significant potential for uncovering intricate interactions in observational data.